How much do you really know about cinema’s most famous blonde? Director Gérald Hustache-Mathieu’s Poupoupidou isn’t a biopic of Marilyn Monroe, but certain details about the life and death of Martine Lingevin, aka Candice Lecoeur, aka cheese poster girl “Belle de Jura” may seem very familiar.

That title is a reference to “I Wanna Be Loved by You”, Marilyn’s famous number from Some Like It Hot. The opening credits seem to be taking their cue from Bert Stern’s Vogue photos – diaphanous top, nipple, bare flesh. It’s just the tip of the iceberg for cinephiles – an appropriate metaphor for a movie set in a snowbound town in Eastern France.

Poupoupidou is one of those films in which the two leading characters never meet because one of them is already dead. Jean-Paul Rouve stars as David Rousseau, a successful crime writer who arrives in the Mouthe to claim a legacy from his dead uncle. (It turns out to be a stuffed dog.) But on his way out of town he sees the corpse of local celebrity Candice (let’s use that name) being exhumed from the snow. He decides to stick around and play detective.

What follows is a mix of quirky comedy and whodunit as Rousseau refuses to believe the official verdict that Candice committed suicide. With some unofficial help from gay cop Bruno (played by Guillaume Gouix), he blunders around town interviewing the dead woman’s friends and colleagues and immersing himself in her extensive diaries.

As the ill-fated Candice, Sophie Quinton isn’t notable for her resemblance to Marilyn. (She looks more like Michelle Williams, who takes on the role of the Blonde Bombshell in My Week with Marilyn.) Quinton plays this model-turned-weather girl as sweet, a bit naïve and always willing to take off her clothes in the interests of her career. But as the Monroe parallels stack up – her doomed relationships with a sportsman, writer and Kennedyesque politician — any sense of who Candice really was becomes less clear.

The screenplay by Hustache-Mathieu and Juliette Sales features some enjoyably terse exchanges between Rousseau and the local police chief (a menacing Olivier Rabourdin). We learn that almost everyone in town is a fan of our amateur sleuth’s literary works, but we don’t get much background on the man himself. Does an early scene at the morgue hint at necrophilia or is Candice just a really good story?

There’s much to enjoy in this stylishly shot movie — particularly if you’re familiar with Monroe’s life story. A risqué scene in which a nude Candice poses with a bunch of equally exposed fireman, is an obvious reference to the famous Monroe calendar shoot. But for me, they went a bit too far re-creating the notorious “Happy Birthday Mr President” number and having Candice expose herself at the end.

Poupoupidou keeps you interested with its tart dialogue, visual gags and those parka-clad cops who might have stepped straight out of Fargo. But there’s little here in the way of action or suspense — apart from a couple of scenes where Rousseau almost gets himself killed.

With the main characters connected by an unwritten book rather than a past relationship, it’s hard to wring any real emotion from the dénouement. It’s Bruno who seems most affected by the fate of Candice. I was left wishing this film had been darker, more edgy and a bit less in thrall to the legend of Marilyn Monroe.